write an inequality relating the given angle measures.
m\angle gef and m\angle hef
choose the correct answer below.
\$ \bigcirc a. m \angle gef=m \angle hef \$
\$ \bigcirc b. m \angle gef\\( \bigcirc c. m \angle gef>m \angle hef \$

Question

write an inequality relating the given angle measures.
m\angle gef and m\angle hef
choose the correct answer below.
$ \bigcirc a. m \angle gef=m \angle hef $
$ \bigcirc b. m \angle gef<m \angle hef $
$ \bigcirc c. m \angle gef>m \angle hef $

Accepted Answer

# Explanation:
## Step1: Recall the Hinge Theorem
The Hinge Theorem states that if two sides of one triangle are congruent to two sides of another triangle, but the third side of the first triangle is shorter than the third side of the second triangle, then the included angle of the first triangle is smaller than the included angle of the second triangle.
In $\triangle GEF$ and $\triangle HEF$, $GE = HE$ (marked with red - cross), $FE=FE$ (common side), and $FG = 10$, $FH = 15$

## Step2: Apply the Hinge Theorem
Since $FG<FH$, by the Hinge Theorem, the included angle $\angle GEF$ (included angle of $FE$ and $GE$ in $\triangle GEF$) and $\angle HEF$ (included angle of $FE$ and $HE$ in $\triangle HEF$) satisfy $m\angle GEF<m\angle HEF$

# Answer:
B. $m\angle GEF < m\angle HEF$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the Hinge Theorem

Step2: Apply the Hinge Theorem

Answer: